Average value of AC over a complete cycle is always zero

[atavistic]

Homework Statement

Statement 1: Average value of AC over a complete cycle is always zero.
Statement 2: Average value of AC is always defined over half cycle.

We need to tell whether these two statements are right, and if 1 is right then whether 2 is its explanation.

Homework Equations

Well arithmetic mean = integral f(x)dx/ integral dx
root mean sqaure = root( integral f(x)^2 dx/ integral dx)

The Attempt at a Solution

I think both are false since it depends upon the type of mean we are taking. Arithmetic would be zero and root mean square non zero. And I think we take mean over complete cycle only. But my answer is wrong.

 

[atavistic]

Is this the right place to post this?

 

[Dr.D]

Who says your answer is wrong? (or right?)

The first statement is pretty clearly true. If you perform a simple average of a sinusoid over one full cycle it comes out zero.

As you observe, it does not make sense to try to average a periodic function over only half of its period, so the second statement does not look correct. If, however, you make an rms calculation over the half period it will be the correct rms value. So the second statement is not clearly right or wrong, but rather seems just vague as to what it means.